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Unformatted text preview: Trevino, Denise Final 1 Due: May 14 2005, 6:00 pm Inst: Turner 1 This print-out should have 28 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. The due time is Central time. 001 (part 1 of 1) 10 points Consider a frictionless roller coaster such as depicted below. The acceleration of gravity is 9 . 8 m / s 2 . 14 m A B C h A Passenger cars start at point A with zero initial speed, accelerate as they go down to point B, swing around the circular vertical loop B C B of radius 14 m, then go on towards further adventures (not shown). When a car goes through the top of the loop (point C), the passengers feel weightless (for just a moment). What is the height h A of the starting point A above the loops bottom B? Correct answer: 35 m. Explanation: Let : R = 14 m and g = 9 . 8 m / s 2 . A passenger feels weightless when his ac- celeration ~a is precisely equal to the free- fall acceleration ~g . At the top of the loop (point C), passengers have no tangential ac- celeration while their normal acceleration is directed straight down and has magnitude a N = v 2 R . Weightlessness happens when this accelera- tion equals g , therefore the cars should go through point C at speed v C = p Rg . In the absence of friction, the mechanical energy of a car is conserved as it follows the coasters route, thus K A + U A = K C + U C = m 2 v 2 A + mg h A = m 2 v 2 C + mg 2 R. Therefore, in light of the initial condition v A = 0, we have mg h A = mg 2 R + m 2 v 2 C = mg 2 R + m 2 Rg = 5 2 mg R h A = 5 2 R = 5 2 (14 m) = 35 m . 002 (part 1 of 1) 10 points Use the potential energy vs . position plot shown below to answer the following question. A particle is released from point A and moves in the potential U ( x ). Suppose the mechanical energy of the system is conserved. x U ( x ) T V Z A At which position(s) will the kinetic energy of the particle have its maximum value? 1. Point V . 2. The particle remains stationary at point A . Trevino, Denise Final 1 Due: May 14 2005, 6:00 pm Inst: Turner 2 3. Points T and Z . 4. Point T . 5. Point Z . correct Explanation: Since the total energy is constant, the max- imum kinetic energy will occur when the po- tential energy is a minimum. Thus point Z is the correct answer. 003 (part 1 of 1) 10 points A particle on a string is whirled in a circle at a constant speed, in the absence of a gravita- tional field. A top view of the circular motion at one instant is v Choose the diagram showing the compo- nents of the acceleration vector at that in- stant. 1. correct 2. 3. 4. 5. 6. 7. 8. 9. Explanation: The force acting on a particle in a circular motion is a central force and points to the center of the circle....
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This note was uploaded on 02/09/2010 for the course PHY 303K taught by Professor Turner during the Spring '08 term at University of Texas at Austin.
- Spring '08